The non-solvsoliton conjecture for deformed symmetric supergravity c-map spaces

Let a symmetric supergravity $c$-map space be a quaternionic Kähler symmetric space of dimension $4n$, and consider its one-loop deformation with parameter $c>0$. Its cohomogeneity-one action has hypersurface orbits equipped with the induced metric; these orbits are solvmanifolds, and a solvsoliton is a solvable homogeneous Ricci soliton.

Non-solvsoliton conjecture. If the one-loop deformation has $c>0$ and dimension $4n>4$, then every hypersurface orbit of its cohomogeneity-one action, with the induced metric, is not a solvsoliton.

The conjecture is motivated by the paper's computations for the considered examples and by results on solvsolitons and their uniqueness. The source gives no evidence that the general statement has been resolved.